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Properties

Label 1210.2.l
Level $1210$
Weight $2$
Character orbit 1210.l
Rep. character $\chi_{1210}(233,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $432$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1210.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1210, [\chi])\).

Total New Old
Modular forms 1776 432 1344
Cusp forms 1392 432 960
Eisenstein series 384 0 384

Trace form

\( 432 q + 8 q^{3} + 8 q^{5} + 20 q^{7} + O(q^{10}) \) \( 432 q + 8 q^{3} + 8 q^{5} + 20 q^{7} + 32 q^{12} + 20 q^{15} + 108 q^{16} + 20 q^{17} + 8 q^{20} + 24 q^{23} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 20 q^{28} - 16 q^{31} + 124 q^{36} - 32 q^{37} + 36 q^{38} + 20 q^{41} + 20 q^{42} - 64 q^{45} - 40 q^{46} - 36 q^{47} - 8 q^{48} - 40 q^{50} - 40 q^{51} - 40 q^{52} - 4 q^{53} + 8 q^{56} - 48 q^{58} - 16 q^{60} - 80 q^{61} - 40 q^{62} - 100 q^{63} + 16 q^{67} - 20 q^{68} + 72 q^{70} + 96 q^{71} + 20 q^{73} + 88 q^{75} - 16 q^{78} + 12 q^{80} + 228 q^{81} + 16 q^{82} + 80 q^{85} + 56 q^{86} + 80 q^{90} + 68 q^{91} + 16 q^{92} - 76 q^{93} - 20 q^{95} - 84 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1210, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)